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From molecular symmetry to order parameters

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The Mathematics of Liquid Crystals

We propose a systematic molecular modeling of liquid crystals, the models can be used to depict isotropic, nematic, smectic, columnar, cholesterics and blue phases. The tensor model can be reduced from molecular model using closure and Taylor expansion, the vector model can be reduced from tensor or molecular model using axial symmetry assumption. Using Newton mechanic and virial expansion, we build a generic molecular model to describe phase behaviors of rigid molecules of arbitrary shape. The system is characterized by a pairwise kernel function. The kernel function can be simplified by the molecular symmetry. Onsager potential is a leading order for rod-like molecular using hard core potential, and Maier-Saupe potential is a good second approximation using Lennard Jones potential. The new models including simplified kernel functions are proposed for bent-core molecules and other shape molecules. We also clarify the criteria of choosing order parameters, both from theoretical aspects and from results of experiments and simulations. According to these criteria, we explain why the eigenvalue of second moment is chosen to describe spatially homogeneous phases of rod-like molecules, and predict the choice of order parameters for bent-core molecules and other molecules of different symmetries. The rigorous analysis for choosing the order parameter will be given for Maier-Saupe model of rod-like molecular.

This talk is part of the Isaac Newton Institute Seminar Series series.

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